Finite Group Databasebeta

← #11784626

Subgroups — #11784626

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4C2×#63580C214yesmaximal, complemented
5#72139—31nomaximal
6#69537—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67C2212yes—
9C2×C3×#235—22no—
10C2×C3×#235—22no—
11C2×C3×#235—28no—
12C22×C3×D12C411yescharacteristic, complemented
13C22×C3×C4×D3C412yescomplemented
14C22×C3×Dic6C411yescharacteristic, complemented
15C2×#3757C2212yes—
16C2×C3×#217C2212yes—
17#63658—22no—
18C3×C3⋊#95—22no—
19#63580—28no—
20C22×C3×#41—31no—
21C22×#235D311yescharacteristic
22C3×#381—31no—
23C2×#834—34no—
24#5211—31no—
25#5211—31no—
26#5211—61no—
27#5211D311yescharacteristic, complemented
28C2×#806—34no—
29C24×C32C2311yescharacteristic
30C23×C3×D3C2×C412yes—
31C22×C32×C4—24no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D412yes—
35C22×C32×C4D412yes—
36C22×C3⋊Dic3—22no—
37C2×C3×#67—22no—
38C2×C3×#67—24no—
39C2×C3×#67—22no—
40C2×C3×#67D418yes—
41C22×C3×Dic3—22no—
42C22×C3×Dic3C2×C412yes—
43C3×#235—216no—
44C3×#235—216no—
45C2×C3×D12—24no—
46C2×C3×D12—22no—
47C2×C3×C4×D3—24no—
48C2×C3×C4×D3—24no—
49C2×C3×C4×D3—24no—
50C2×C3×Dic6—22no—
51C2×C3×Dic6—24no—
52#3757—24no—
53C3×#217—24no—
54#1782—91noSylow
55C2×C3×#41—68no—
56C2×C3×#41—62no—
57C2×C3×#41—62no—
58C22×C3×Q8—31no—
59C22×C3×D4—32no—
60C22×C3×D4—31no—
61C23×C3×C4—21no—
62C23×C3×C4—32no—
63C23×C3×C4C2×D311yescharacteristic
64C23×C3×C4C2×D311yescharacteristic
65C22×#67C2×D312yes—
66C2×#235—22no—
67C2×#235—22no—
68C2×#235—28no—
69C22×D12Dic311yescharacteristic, complemented
70C22×C4×D3Dic312yescomplemented
71C22×Dic6Dic311yescharacteristic, complemented
72C2×C3×C22⋊C4—32no—
73C2×#217—32no—
74C2×#217—32no—
75C2×#217—62no—
76C2×#217C2×D312yes—
77C3×#95—62no—
78#834—68no—
79C3⋊#95—22no—
80C3⋊#95—64no—
81C3⋊#95—62no—
82C3⋊#95—62no—
83#806—68no—
84C23×C32—42no—
85C23×C32C22×C411yescharacteristic
86C23×C32C2×D411yescharacteristic
87C23×C32C2×D414yes—
88C23×C32C2×D411yescharacteristic
89C22×C3×D3—22no—
90C22×C3×D3—22no—
91C22×C3×D3—44no—
92C22×C3×D3C22⋊C414yes—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—24no—
97C2×C32×C4C22⋊C412yes—
98C2×C32×C4C22⋊C412yes—
99C2×C3⋊Dic3—44no—
100C2×C3⋊Dic3—42no—
101C3×#67—28no—
102C3×#67—28no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—44no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3C22⋊C414yes—
108C3×D12—28no—
109C3×C4×D3—216no—
110C3×Dic6—28no—
111C22×#41—31no—
112C2×#99—94no—
113#381—31no—
114#381—91no—
115C24×C3—21no—
116C24×C3—32no—
117C24×C3C22×D311yescharacteristic
118C24×C3C22×D311yescharacteristic
119C23×D3C2×Dic312yes—
120C3×#41—616no—
121C3×#41—616no—
122C2×C3×Q8—64no—
123C2×C3×Q8—62no—
124C2×C3×D4—38no—
125C2×C3×D4—64no—
126C2×C3×D4—62no—
127C2×C3×D4—64no—
128C2×C3×D4—62no—
129C2×C3×D4—62no—
130C22×C3×C4—24no—
131C22×C3×C4—24no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—32no—
137C22×C3×C4—44no—
138C22×C3×C4—64no—
139C22×C3×C4—64no—
140C22×C3×C4—64no—
141C22×C3×C4—62no—
142C22×C3×C4C4×D311yescharacteristic
143C22×C3×C4C4×D311yescharacteristic
144C22×C3×C4D1212yes—
145C22×C3×C4C2×Dic311yescharacteristic
146C22×C3×C4C2×Dic311yescharacteristic
147C22×C3×C4#6712yes—
148C22×C3×C4#6712yes—
149C22×C3×C4#6712yes—
150C2×#67—22no—
151C2×#67—22no—
152C2×#67—24no—
153C2×#67#6718yes—
154C22×Dic3—22no—
155C22×Dic3—64no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C22×Dic3C2×Dic312yes—
159#235—216no—
160#235—216no—
161C2×D12—24no—
162C2×D12—22no—
163C2×C4×D3—24no—
164C2×C4×D3—24no—
165C2×C4×D3—24no—
166C2×Dic6—22no—
167C2×Dic6—24no—
168C3×C22⋊C4—64no—
169#217—24no—
170#217—64no—
171#217—64no—
172#217—124no—
173C22×C32—22no—
174C22×C32—22no—
175C22×C32—22no—
176C22×C32—44no—
177C22×C32C2×C22⋊C412yes—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12012yes—
180C22×C32#12012yes—
181C2×C3×D3—24no—
182C2×C3×D3—44no—
183C2×C3×D3—44no—
184C2×C3×D3—44no—
185C32×C4—22no—
186C32×C4—22no—
187C3⋊Dic3—82no—
188C3×Dic3—24no—
189C3×Dic3—82no—
190C2×#41—68no—
191C2×#41—62no—
192C2×#41—62no—
193C22×Q8—31no—
194C22×D4—32no—
195C22×D4—31no—
196C23×C4—32no—
197C23×C4D3211yescharacteristic
198C2×C22⋊C4—32no—
199C2×C22⋊C4—92no—
200#99—188no—
201#95—62no—
202#95—182no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—24no—
207C23×C3—34no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—44no—
211C23×C3—62no—
212C23×C3—62no—
213C23×C3—124no—
214C23×C3C2×C4×D311yescharacteristic
215C23×C3C2×D1211yescharacteristic
216C23×C3D3×D414yes—
217C23×C3C22×Dic311yescharacteristic
218C23×C3C2×#6711yescharacteristic
219C23×C3C2×#6711yescharacteristic
220C23×C3C2×#6711yescharacteristic
221C23×C3C2×#6714yes—
222C22×D3—22no—
223C22×D3—22no—
224C22×D3—44no—
225C22×D3#21714yes—
226C3×Q8—68no—
227C3×D4—68no—
228C3×D4—68no—
229C3×D4—68no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—34no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—616no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—124no—
249C2×C3×C4—122no—
250C2×C3×C4(C2×D3)⋊C412yes—
251C2×C3×C4(C2×D3)⋊C412yes—
252C2×C3×C4#21712yes—
253C2×C3×C4#21712yes—
254#67—28no—
255#67—28no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—44no—
259C2×Dic3—42no—
260C2×Dic3—124no—
261C2×Dic3—128no—
262C2×Dic3—124no—
263C2×Dic3—124no—
264C2×Dic3—122no—
265C2×Dic3—122no—
266C2×Dic3#21714yes—
267D12—28no—
268C4×D3—216no—
269Dic6—28no—
270C2×C32—22no—
271C2×C32—22no—
272C2×C32—22no—
273C2×C32#37911yescharacteristic
274C2×C32#41012yes—
275C3×D3—44no—
276C24—32no—
277C24C2×D3211yescharacteristic
278#41—616no—
279#41—616no—
280C2×Q8—64no—
281C2×Q8—62no—
282C2×D4—38no—
283C2×D4—64no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—64no—
287C2×D4—62no—
288C22×C4—24no—
289C22×C4—32no—
290C22×C4—64no—
291C22×C4—64no—
292C22×C4—64no—
293C22×C4—62no—
294C22×C4—182no—
295C22×C4D3×Dic311yescharacteristic
296C22×C4D3×Dic311yescharacteristic
297C22×C4#62512yes—
298C22×C4#62612yes—
299C22⋊C4—64no—
300C22⋊C4—184no—
301C22×C3—24no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—44no—
315C22×C3—44no—
316C22×C3—48no—
317C22×C3—64no—
318C22×C3—124no—
319C22×C3—124no—
320C22×C3—124no—
321C22×C3D3×C22⋊C412yes—
322C22×C3#88212yes—
323C22×C3C2×(C2×D3)⋊C411yescharacteristic
324C22×C3#93712yes—
325C22×C3C2×#21711yescharacteristic
326C22×C3C2×#21712yes—
327C22×C3#95312yes—
328C22×C3#95312yes—
329C2×D3—24no—
330C2×D3—44no—
331C2×D3—44no—
332C2×D3—44no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—42no—
338C3×C4—42no—
339C3×C4—64no—
340C3×C4—242no—
341Dic3—24no—
342Dic3—82no—
343Dic3—244no—
344Dic3—242no—
345Dic3—242no—
346C32#178211yescharacteristic, complemented, Sylow
347C23—34no—
348C23—42no—
349C23—62no—
350C23—62no—
351C23—124no—
352C23C2×D3×Dic311yescharacteristic
353C23C2×#62511yescharacteristic
354C23C2×#62611yescharacteristic
355C23D3×#6714yes—
356Q8—68no—
357D4—68no—
358D4—68no—
359D4—68no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—34no—
365C2×C4—616no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—124no—
369C2×C4—122no—
370C2×C4—364no—
371C2×C4—362no—
372C2×C4(C2×D3)⋊Dic312yes—
373C2×C4(C2×D3)⋊Dic312yes—
374C2×C3—24no—
375C2×C3—22no—
376C2×C3—22no—
377C2×C3—22no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3—22no—
383C2×C3—42no—
384C2×C3—42no—
385C2×C3—124no—
386C2×C3#495511yescharacteristic
387C2×C3#500612yes—
388C2×C3#524012yes—
389C2×C3#524711yescharacteristic
390D3—44no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—44no—
395C22—64no—
396C22—124no—
397C22—124no—
398C22—124no—
399C22C2×(C2×D3)⋊Dic311yescharacteristic
400C22D3×#21712yes—
401C22#6397612yes—
402C22#6397712yes—
403C4—22no—
404C4—22no—
405C4—64no—
406C4—242no—
407C4—722no—
408C3—21no—
409C3#6953711yescharacteristic, complemented
410C3#7213911yescharacteristic, complemented
411C2—22no—
412C2—22no—
413C2—22no—
414C2—124no—
415C2#1059123112yes—
416C2#1059170611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#235C2
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1782
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592910C2semidirect
3. C3×#5211C2semidirect
4. C2×#63580C2semidirect
12. C22×C3×D12C4semidirect
13. C22×C3×C4×D3C4semidirect
14. C22×C3×Dic6C4semidirect
27. #5211D3semidirect
69. C22×D12Dic3semidirect
70. C22×C4×D3Dic3semidirect
71. C22×Dic6Dic3semidirect
346. C32#1782semidirect
409. C3#69537semidirect
410. C3#72139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#2352
#105929102
C3×#52112
C2×#635802
#721393
#695373